Find a minimum weighted spanning tree of the Cycle graph

Question

I'm trying to solve the problem presented above and here is my attempt:

Attempt: We can apply Dijkstra's shortest path algorithm instead of using Prim's and Kruskal's algorithms to find a MST as Dijkstra will visit all the nodes in the smallest weighted distance. Complexity: For G = (V,E), O(E log(V))

Questions:

(1) Is my approach correct ? (2) Is it the most efficient answer to the question ?

If i'm completely wrong, I would appreciate a correct and efficient solution.

Answer 1

A cycle graph contains no edges other than those connecting the vertices in the cycle. So what we can do is iterate through all N edges and eliminate the maximum weighted edge forming a spanning tree of N - 1 edges containing the minimum sum of edges, forming a Minimum Spanning Tree.